Activity:

Begin by showing students how exponents represent repeated multiplication by using the blocks. For example, arrange blocks to represent 3^2 (three groups of three blocks) and 3^3 (three groups of three groups of three).

Let students physically group and stack blocks to visualize what 2^1, 2^2, 2^3, etc., look like in terms of growth. Encourage students to see how the number of blocks increases significantly with each added exponent.

Discussion: Ask students to explain what happens to the block groups as the exponent increases. Guide them to understand that exponents increase numbers rapidly because they represent repeated multiplication, not addition.

Activity:

Transition from physical blocks to drawing representations on graph paper. Students draw squares to represent values like 2^2 and 3^2 and draw cubes or use grid blocks for values like 2^3 and 3^3.

Have students label each exponent expression and calculate the total to see the numerical result, reinforcing the idea that exponents grow exponentially.

Visualization of Powers of 10: For values like 10^1, 10^2, 10^3, etc., show how each step represents "adding a zero," reinforcing the pattern of rapid growth in powers of ten. This can be drawn on graph paper in rows or columns.

Discussion: Discuss how the drawings on paper relate to the physical blocks and why the quantities increase so much as exponents rise.

Activity:

Move to solving exponential expressions without manipulatives or drawings. Give students a set of exponent expressions to evaluate, such as 2^3, 5^2, 10^4, and 3^5, and encourage them to solve these either mentally or with paper.

Have students apply exponent rules, like the product rule (a^m * a^n = a^(m+n)) and the power rule ((a^m)^n = a^(m * n)), using examples to reinforce each rule.

Challenge Activity: Present simple real-world examples where exponential growth is relevant, such as doubling bacteria (using 2^n) and ask students to predict the growth at certain time intervals.

Reflection: Ask students to reflect on how they used physical and representational tools to understand abstract exponents. Encourage them to verbalize what exponents mean to them now, consolidating the conceptual understanding they’ve built through the CRA stages.